If you can freely enter characters into turn order, just enter them again and again, based on speed. You might want to convert speed into something that lines up to whatever you use for turn ordering.
So, if your speed is from 1-6 you might use 10-speed as a counter between turns of a character. A speed 3 character would act at 7, 14, 21, 28, a speed 6 character at 4 8 12 16 20 24 28, and a speed 1 character at 9, 18, 27
Adjust numbers to balance how impactful you want speed to be. You can also enter "turn end" or environment events at 10, 20, 30.
Acting first in a turn based combat has advantages, but you will get to a point where having more speed is not benefitial, since you already act first. But do not underestimate those advantages for balancing. Having a character act twice as often as others would have a huge impact. But I guess doing twice as much damage would have the same impact. Pun intended. But acting first can make the difference between losing and winning, so that's hard to evaluate as an advantage. Act first, stun your enemy, win the fight. Act second, get stunned, lose the fight.
But this is all part of balancing hero ressources against enemy difficulty. And I did not understand the just as impactful part and the thing with the cycles and how a turn based system would flow continously.